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This paper deals with three test statistics for testing a linear hypothesis and estimators of regression coe1⁄2cients in the GMANOVA model which was proposed by Potthof and Roy (1964), without assuming normal error. The test statistics considered include the likelihood ratio statistic, the Lawley-Hotelling trace criterion and the Bartlett-Nanda-Pillai trace criterion, which have been proposed under normality. We obtain asymptotic expansions of the null distributions of three test statistics up to the order nÿ1, where n is the sample size. The results are generalizations of the formulas in Wakaki, Yanagihara and Fujikoshi (2000). In addition, asymptotic expansions of the distribution functions of several standardized statistics on regression coe1⁄2cients are derived.

Asymptotic expansions of the null distributions of three test statistics in a nonnormal {GMANOVA} model